CBSE Class 12 Mathematics Applications of Integration Assignment Set 01

Question. The area of the region described by A{(x, y) : x² + y² ≤ 1 and y² ≤ 1- x is:
(a) π/2 - 2/3
(b) π/2 + 2/3
(c) π/2 + 4/3
(d) π/2 - 3/4
Answer : C

Question. The area (in sq. units) of the region bounded by the curve x² = 4y and the straight line x = 4y – 2 is :
(a) 5/4
(b) 9/8
(c) 7/8
(d) 3/4
Answer : B

Question. The area of the region (in sq. units), in the first quadrant bounded by the parabola y = 9x² and the lines x = 0, y = l and y = 4, is :
(a) 7/9
(b) 14/3
(c) 7/3
(d) 14/9
Answer : D

Question. The area of the region bounded by the curves y =| x - 2 |, x = 1, x = 3 and the x-axis is 
(a) 4
(b) 2
(c) 3
(d) 1
Answer : D

Question. The area between the parabolas x² = y/4 = and x² = 9y and the straight line y = 2 is : 
(a) 20√2
(b) 10√2/3
(c) 20√2/3
(d) 10√2
Answer : C

Question. If a straight line y – x = 2 divides the region x² + y ≤ 4 into two parts, then the ratio of the area of the smaller part to the area of the greater part is
(a) 3π – 8 : π + 8
(b) π – 3 : 3π + 3
(c) 3π – 4 : π + 4
(d) π – 2 : 3π + 2
Answer : D

Question. The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and x = 3π/2 p is
(a) 4√2 + 2
(b) 4√2 -1
(c) 4√2 +1
(d) 4√2 - 2
Answer : D

Question. The area of the region bounded by the parabola (y – 2)² = x –1, the tangent of the parabola at the point (2, 3) and the x-axis is: 
(a) 6
(b) 9
(c) 12
(d) 3
Answer : B

Question. The area enclosed by the curves y = x², y = x³, x = 0 and x = p, where p > 1, is 1/6. The p equals
(a) 8/3
(b) 16/3
(c) 2
(d) 4/3
Answer : D

Question. The area of the region enclosed by the curves y = x, x = e, y = 1/x and the positive x-axis is 
(a) 1 square unit
(b) 3/2 square units
(c) 5/2 square units
(d) 1/2 square unit
Answer : B

Question. The area of the plane region bounded by the curves x + 2y² = 0 and x + 3y² = 1is equal to
(a) 5/3
(b) 1/3
(c) 2/3
(d) 4/3
Answer : D

Question. The area of the region bounded by the curve y = x³, and the lines, y = 8, and x = 0, is
(a) 8
(b) 12
(c) 10
(d) 16
Answer : B

Question. The area (in square units) bounded by the curves y = √x , 2y – x + 3 = 0, x-axis, and lying in the first quadrant is :
(a) 9
(b) 36
(c) 18
(d) 27/4
Answer : A

Question. The area enclosed between the curves y² = x and y = | x | is
(a) 1/6
(b) 1/3
(c) 2/3
(d) 1
Answer : A

Question. The area bounded by the curves y² = 4x and x² = 4y is:
(a) 32/3 sq units
(b) 16/3 sq units
(c) 8/3 sq. units
(d) 0 sq. units
Answer : B

Question. The area bounded by the curves y = lnx, y = ln |x|,y = | ln x | and y = | ln |x| | is 
(a) 4sq. units
(b) 6 sq. units
(c) 10 sq. units
(d) none of these
Answer : A